| Title:
|
Lexicographic product decompositions of half linearly ordered loops (English) |
| Author:
|
Demko, Milan |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
57 |
| Issue:
|
2 |
| Year:
|
2007 |
| Pages:
|
607-629 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we prove for an hl-loop $Q$ an assertion analogous to the result of Jakubík concerning lexicographic products of half linearly ordered groups. We found conditions under which any two lexicographic product decompositions of an hl-loop $Q$ with a finite number of lexicographic factors have isomorphic refinements. (English) |
| Keyword:
|
half linearly ordered quasigroup |
| Keyword:
|
half linearly ordered loop |
| Keyword:
|
lexicographic product |
| Keyword:
|
isomorphic refinements |
| MSC:
|
06F99 |
| MSC:
|
20N05 |
| idZBL:
|
Zbl 1174.06325 |
| idMR:
|
MR2337618 |
| . |
| Date available:
|
2009-09-24T11:47:59Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128193 |
| . |
| Reference:
|
[1] V. D. Belousov: Foundations of the theory of quasigroups and loops.Nauka Moscow, 1967. (Russian) MR 0218483 |
| Reference:
|
[2] Š. Černák: Lexicographic products of cyclically ordered groups.Math. Slovaca 45 (1995), 29–38. MR 1335837 |
| Reference:
|
[3] M. Demko: Lexicographic product decompositions of partially ordered quasigroups.Math. Slovaca 51 (2001), 13–24. Zbl 0986.06012, MR 1817719 |
| Reference:
|
[4] M. Demko: On half linearly ordered quasigroups.Acta Facultatis Prešov 39 (2002), 39–45. |
| Reference:
|
[5] L. Fuchs: Partially ordered algebraic systems.Pergamon Press, Oxford-London-New York-Paris, 1963. Zbl 0137.02001, MR 0171864 |
| Reference:
|
[6] M. Giraudet and F. Lucas: Groupes à moitié ordonnés.Fund. Math. 139 (1991), 75–89. MR 1150592, 10.4064/fm-139-2-75-89 |
| Reference:
|
[7] J. Jakubík: Lexicographic products of partially ordered groupoids.Czech. Math. J. 14 (1964), 281–305. (Russian) MR 0167558 |
| Reference:
|
[8] J. Jakubík: Lexicographic product decompositions of cyclically ordered groups.Czech. Math. J. 48 (1998), 229–241. MR 1624307, 10.1023/A:1022881202595 |
| Reference:
|
[9] J. Jakubík: Lexicographic products of half linearly ordered groups.Czech. Math. J. 51 (2001), 127–138. MR 1814638, 10.1023/A:1013761906636 |
| Reference:
|
[10] A. I. Maltsev: On ordered group.Izv. Akad. Nauk SSSR, Ser. Matem. 13 (1949), 473–482. (Russian) |
| . |
